Evaluate: tan7∘tan23∘tan60∘tan67∘tan83∘

tan7∘tan23∘tan60∘tan67∘tan83∘=tan7∘.tan23∘.3.tan(90∘−23∘).tan(90∘−7∘) [∵tan(90∘−θ)=cotθ ]==tan7∘.tan23∘.3.cot23∘.cot7∘tan7∘.cot7∘tan23∘.cot23∘.3 (∵tanθ.cotθ=1)=1×1×3=3

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Evaluate: 7^{} 23^{} 60^{} 67{^{}} 83^{}

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Evaluate: $tan 7^{\circ} tan 2 3^{\circ} tan 6 0^{\circ} tan 67^{\circ} tan 8 3^{\circ}$

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Text solutionVerified

tan 7^{\circ} tan 2 3^{\circ} tan 6 0^{\circ} tan 67^{\circ} tan 8 3^{\circ}

= tan 7^{\circ} . tan 2 3^{\circ} . 3 . tan (9 0^{\circ} - 2 3^{\circ}) . tan (9 0^{\circ} - 7^{\circ})

[∵ tan (9 0^{\circ} - θ) = cot θ]

= tan 7^{\circ} . tan 2 3^{\circ} . 3 . cot 2 3^{\circ} . cot 7^{\circ}

tan 7^{\circ} . cot 7^{\circ} tan 2 3^{\circ} . cot 2 3^{\circ} . 3

(∵ tan θ . cot θ = 1)

= 1 \times 1 \times 3 = 3

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Question Text	Evaluate: $tan 7^{\circ} tan 2 3^{\circ} tan 6 0^{\circ} tan 67^{\circ} tan 8 3^{\circ}$
Answer Type	Text solution:1
Upvotes	150

Evaluate: tan7∘tan23∘tan60∘tan67∘tan83∘

Text solutionVerified

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Evaluate: $tan 7^{\circ} tan 2 3^{\circ} tan 6 0^{\circ} tan 67^{\circ} tan 8 3^{\circ}$